Properties

Label 63175.a
Number of curves $1$
Conductor $63175$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 63175.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
63175.a1 63175z1 \([0, 0, 1, 3294125, 2052341406]\) \(43022168064/44700103\) \(-4107335403175279296875\) \([]\) \(10713600\) \(2.8340\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 63175.a1 has rank \(0\).

Complex multiplication

The elliptic curves in class 63175.a do not have complex multiplication.

Modular form 63175.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} - 3 q^{3} + 2 q^{4} + 6 q^{6} + q^{7} + 6 q^{9} + 5 q^{11} - 6 q^{12} + 5 q^{13} - 2 q^{14} - 4 q^{16} + q^{17} - 12 q^{18} + O(q^{20})\) Copy content Toggle raw display